Problem: Ben is $4$ times as old as Ishaan. $6$ years ago, Ben was $6$ times as old as Ishaan. How old is Ishaan now?
Explanation: We can use the given information to write down two equations that describe the ages of Ben and Ishaan. Let Ben's current age be $b$ and Ishaan's current age be $i$. The information in the first sentence can be expressed in the following equation: ${b = 4i}$ Six years ago, Ben was $b - 6$ years old, and Ishaan was $i - 6$ years old. The information in the second sentence can be expressed in the following equation: ${b - 6 = 6(i - 6)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$, it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: ${b = 4i}$. Substituting this into our second equation, we get: ${4i} {-6 = 6(i - 6)}$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $4 i - 6 = 6 i - 36$. Solving for $i$, we get: $2 i = 30.$ $i = 15$.